Question:
Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $10440
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $10440 – $5800 = $4640
Thus, Simple Interest = $4640
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 4640/5800 × 10
= 464000/58000
= 8 years (using formula)
Thus, Time (T) = 8 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $5800
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $4640 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 10% of Principal
= 10% of $5800
= 10/100 × 5800
= 10 × 5800/100
= 58000/100 = 580
Thus, simple Interest for 1 year = $580
Now,
∵ If the simple Interest is $580, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/580 years
∴ If the simple Interest is $4640, then the time = 1/580 × 4640 years
= 1 × 4640/580 years
= 4640/580 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.
(2) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(3) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?
(5) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(7) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(10) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.